Manuscript XVI-I@1 · XVI-I.tex · proposition · a7046a8d

Proposition: Free variation of the prepared polynomial

Off-shell representatives, free variation, and quantum limits › Free derivation with preparation held fixed · lines 1542–1560 · proof included or linked

XVI-I@1#prop:s0, XVI-I@1#eq:s0

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With that convention,

s_{0} F_{t} (h, ϕ) = 2 ⟨ t_{D}, (R c) \otimes h \otimes ϕ ⟩ .

No vanishing of the right-hand side is asserted.

Proof. Only the two tensor arguments vary. The scalar variation is zero, and tensor-slot symmetry makes the two tensor contributions equal. Compact support makes the pairing with smooth directions well defined.

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XVI-I@1#eq:s0 · line 1545
$s_{0} F_{t} (h, ϕ) = 2 ⟨ t_{D}, (R c) \otimes h \otimes ϕ ⟩ .$

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section: Free derivation with preparation held fixed
section: Free derivation with preparation held fixed